Problem 8 - Algebra and Trigonometry

Question

Factor out the greatest common factor. $$x(2 x+1)+4(2 x+1)$$

Step-by-Step Solution

Answer

The factored form of the expression is \((x+4)(2x + 1)\).

Step 1: Recognizing the Common Factor

First, observe the expression \(x(2 x+1)+4(2 x+1)\). The two terms here, \(x(2 x+1)\) and \(4(2 x+1)\), share a common factor of \(2x + 1\).

Step 2: Factoring out the Common Factor

Next, factor out the common factor \(2x + 1\) from the expression. This means that the \(2x + 1\) in each term is separated out, leaving behind the coefficients \(x\) and \(4\). So the expression becomes \((x+4)(2x + 1)\).

Step 3: Final Expression

The final factored form of the expression is therefore \((x+4)(2x + 1)\).